An inventor claims to have developed a power cycle operating between hot and cold reservoirs at 1350 K and 295 K, respectively, that provides a steady-state power output of (a) 30.00 kW, (b) 33.33 kW, while receiving energy by heat transfer from the hot reservoir at the rate 150,000 kJ/h. Evaluate each claim.

Question

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Respuesta :

DeniceSandidge DeniceSandidge · Answer 1 · 2020-04-16T13:13:19+02:00

Answer:

efficiency = 0.71999 < 0.78148

efficiency = 0.7999 ≈ 0.78148

Explanation:

given data

Hot reservoir Temp Th = 1350 K

Cold reservoir Temp Tc = 295 K

heat transfer rate = 150,000 kJ/h

solution

first we get here maximum possible efficiency that is express as

maximum possible efficiency = 1 - [tex]\frac{Tc}{Th}[/tex] ..........1

put here value and we get

maximum possible efficiency = 1 - [tex]\frac{295}{1350}[/tex]

maximum possible efficiency = 0.78148

and

efficiency = [tex]\frac{Wout}{Qin}[/tex] .................2

here Qin = [tex]\frac{150000}{3600}[/tex] = 41.667

so put here value in equation 2 we get

efficiency = [tex]\frac{30}{41.667}[/tex]

efficiency = 0.71999 < 0.78148

and

efficiency = [tex]\frac{33.33}{41.667}[/tex]

efficiency = 0.7999 ≈ 0.78148

claim might be true or not because there always be looser